Expression of type Equals

from the theory of proveit.numbers.summation

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, k
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, nine, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = subtract(k, two)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(a, nine)), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(a, subtract(nine, one))), subtract(nine, two)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\sum_{k = a}^{9} \left(k - 2\right)\right) = \left(\left(\sum_{k = a}^{9 - 1} \left(k - 2\right)\right) + \left(9 - 2\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 11 operand: 7
4	Operation	operator: 35 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 27 body: 10
8	Operation	operator: 11 operand: 15
9	Operation	operator: 35 operands: 13
10	Conditional	value: 20 condition: 14
11	Literal
12	ExprTuple	15
13	ExprTuple	37, 26
14	Operation	operator: 24 operands: 16
15	Lambda	parameter: 27 body: 18
16	ExprTuple	27, 19
17	ExprTuple	27
18	Conditional	value: 20 condition: 21
19	Operation	operator: 30 operands: 22
20	Operation	operator: 35 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	33, 37
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 39 operand: 32
27	Variable
28	Operation	operator: 30 operands: 31
29	ExprTuple	32
30	Literal
31	ExprTuple	33, 34
32	Literal
33	Variable
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal